A one-dimensional cellular automaton with conservative dynamics is studied. The automaton are a special case of the Boghosian-Levermore model, a probabilistic automaton, that has been used as a microscopic approximation for the Burgers equation. We study the stationary measures, the hydrodynamical limit and the existence of a microscopic interface.
"Shocks in Asymmetric Exclusion Automata." Ann. Appl. Probab. 2 (4) 928 - 941, November, 1992. https://doi.org/10.1214/aoap/1177005581